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Marilyn vos Savant and the Monty Hall Problem (2015)

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Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#51

Post by bemusedthrow75 »

nickpsecurity wrote: post #28
bemusedthrow75 wrote: post #21

This is something I remember from the time. I could not grasp the probability maths (still shit at it, sorry Ms Von Savant) but I could write a program to experimentally demonstrate it, so I did. In QBasic. Because that's what we had and we were happy.

That’s exactly what I did. In FreeBASIC. The way the problem works started coming together in my head as I coded it. The code’s structure reflected the problem’s structure. I realized I previously misunderstood something about the problem statement. Later, I read someone saying many mathematicians got this problem wrong because of how it’s worded. So, it may be challenging, not because probability was challenging, bu…

It's not unclearly specified. It's very tight.

People who get it wrong are usually projecting some implied understanding onto it, which is why they get it wrong.

Which is the point of the problem. It's designed to reveal this tendency in analytical thinking leading to unexpected outcomes. You get it wrong, you're gobsmacked, you understand why, you gain some enlightenment from it. It's fun to be wrong in ways you later understand. (This is one of the thrills of programming: that moment during debugging when you shriek with joy: "YES, IT BROKE!")

The fact that it also exposes the way some overly confident people lash out with anger that exposes other biases is the point of the article, I think.

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#52

Post by bemusedthrow75 »

wizerdrobe wrote: post #49
bemusedthrow75 wrote: post #41

Earlier quoted context omitted.

> Of the cited hate mail Savant received, I have to wonder how many were setup with poor writing on the topic. Have you spent at least equal time considering, given the tenor of much of it, how many were instead willingly exposing their simple misogyny? You might be a bit younger than me, but I remember this well, and I remember this being one of my first introductions into the idea that men who are wrong will lash o…

Interestingly I’ve correctly grow up more recently such that I instead see internet simps here rather than academic misogny as notable, seeing as the tables have largely socially turned since your (I assume by the username) birth year of 1875.

Yes indeed. I and others surely see from this comment that you're a fully mature thinker.

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#53

Post by bemusedthrow75 »

Workaccount2 wrote: post #46

Total aside here, but this article is a good example of the problem, so I just want to point it out. People go digging, usually pretty hard, to find insults to use as capital in whatever point they are trying to make. In this case, yes, she received a lot of criticism and ad-hominem attacks for her correct answer. But she wasn't really criticized for being a woman, despite it being repeated multiple times in the arti…

> But she wasn't really criticized for being a woman

Nobody is saying she was criticised for being a woman, though. What they are observing is that it was the basis of and the tenor of attacks on her character, intelligence, certainty etc.

It was nasty and it really happened, is all I'm saying. Are we better? I hope so. But I don't know that I think so.

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#54

Post by xorcist »

Jimmc414 wrote: post #35

I never understood this one. Not choosing a new door seems like an implied 50/50 choice to keep your original selection. edit: I know it works out on paper, but if I put myself in the situation, I know that if I decided not to choose again that is a choice and I am re-choosing the same door.

It is, strictly as written. The wording, both in the original article and the many rewrites, does not fully explain the problem as intended. The show host not only knows where the prize is, but actively chooses never to reveal the door where the prize is. The reveal is not random. The reveal is a tell where the prize isn't!

Worded more carefully, the answer is more intuitive, and this is probably why there was controversy surrounding it.

The naming is taken from an actual game show, which perhaps confusingly seems to have been a third variant on the same problem, using more steps and trick monetary incentives to make fore more exciting viewing.

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#55

Post by paulcole »

bemusedthrow75 wrote: post #22
tromp wrote: post #12

Earlier quoted context omitted.

It might be that he only does the reveal-and-switch offer if your original pick was the car.

You don't need to know whether he does or does not do that all the time. Because he did it this time? Amazed this nitpicking is still going on; it's illustrative.

I once had somebody claim the answer was wrong because we weren't sure if the contestant wanted the car or the goat.

This puzzle is like a shibboleth for nitpickers.

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#56

Post by mithr »

gerad wrote: post #39

The intuitive way for me to understand the Monte Hall problem is to pretended there are 1000 doors. You pick 1. There’s a 1 in 1000 chance you get it right. The host then opens 998 doors that don’t have the prize. Do you keep your original or do you switch? Are the odds 50:50?

I think the reason it's so hard to understand is that we try to break the problem down into more digestible problems, and in this case, if you only consider the last stage of the game, it certainly seems like it should be 50:50 odds.

In other words, at the final round, you are presented with two doors. Ignore the fact that you already chose one, and assume you were starting at this point: you enter the game, see two doors, and need to pick the one you think hides a car. So intuitively, your odds of choosing which of two doors has the car are 1/2.

It's hard to really understand why it matters that the previous rounds occurred at all — why it matters how you narrowed the selection to these two doors. I don't think the 1000 door version makes that easier to understand, because the same thing is true there — if you come into a game, see two doors, and are asked to choose between them, it's very hard to understand why it matters whether in a previous round there were 2, 3, 10, or 1000 doors — there are only two now, when you make your choice.

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#57

Post by WarOnPrivacy »

kevinmchugh wrote: post #24
swayvil wrote: post #5

Am I the only person who wonders how "Marilyn Vos Savant" also happens to be the smartest person? If you didn't notice, "Savant" means smart. So is it just a coincidence? Karma? The pressure of carrying such a name drove her to smartness?

The "smartest person in the world" tag is a marketing push. It works with her name. It wouldn't work as well if she was named Marilyn Smith.

> The "smartest person in the world" tag is a marketing push.

It reflects some broad understandings of the 1980s and what we valued.

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#58

Post by abeppu »

wizerdrobe wrote: post #11
paulcole wrote: post #7

Earlier quoted context omitted.

What part of the scenario is poorly written in your opinion?

TFA is very well written, but in almost every reproduction of the Monty Hall problem you’ll find it very poorly written such that one would reasonably be led to believe the question is “if I have two doors what is the probability.” Don’t believe me, go search for memes presenting the problem. It’s been on the internet for decades at this point. The setup is near always to send a poor rewrite then link you to a story…

> Of the cited hate mail Savant received, I have to wonder how many were setup with poor writing on the topic.

The article includes the specific wording that Savant used in her column. It seems pretty clear.

> I think this story in its entirety says a lot about ignoring the importance of good technical writing… and how people on the internet love tricking others to feel “right.”

... or, since the column that provoked all hate mail was in 1990 and people saw it in print publications, perhaps it says very little about the internet. And given the higher effort of writing an actual letter to Savant then vs now, it says that people's desire to "correct" a woman is pretty high.

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#59

Post by bemusedthrow75 »

niklasbuschmann wrote: post #42

> Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice? Without additional assumptions this original wording is not cle…

> Without additional assumptions this original wording is not clear

The only problem you are being asked to solve is the one described only in the words of the problem.

That's actually what this is all about. This is a learning exercise, not just about probability, but about comprehension of what the problem as described exactly says.

That's what makes it so enormously valuable.

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#60

Post by btilly »

As stated, the answer is indeterminate. To demonstrate, consider these scenarios.

- Savant's Monty: The host knows where the car is, and wants to prolong the game. Switching wins 2/3 of the time.

- Ignorant Monty: The host has no idea where the car is. Revealing the goat was luck and your odds remain 50-50.

- Malicious Monty: The host knows where the car is, and wants you to lose. The fact that the host didn't reveal the car means that you have the right door. You'll have no chance of winning if you switch.

Nowhere in the problem are Monty's knowledge and motivation stated. When explained, most go along with the assumptions that Savant's argument introduces. When the actual Monty was asked, it turned out that he was usually ignorant. And the malicious scenario demonstrates how different the answer can be.

The fact that all three answers are consistent with the statement of the problem means that it is indeterminate.

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